Recording, analysis, and function of dendritic voltage-gated channels

Estimation of persistent sodium-current density in rat hippocampal mossy fibre boutons: Correction of space-clamp errors

We used whole-cell patch clamp to estimate the stationary voltage dependence of persistent sodium-current density (iNaP) in rat hippocampal mossy fibre boutons. Cox's method for correcting space-clamp errors was extended to the case of an isopotential compartment with attached neurites. The method was applied to voltage-ramp experiments, in which iNaP is assumed to gate instantaneously. The raw estimates of iNaP led to predicted clamp currents that were at variance with observation, hence an algorithm was devised to improve these estimates. Optionally, the method also allows an estimate of the membrane specific capacitance, although values of the axial resistivity and seal resistance must be provided. Assuming that membrane specific capacitance and axial resistivity were constant, we conclude that seal resistance continued to fall after adding TTX to the bath. This might have been attributable to a further deterioration of the seal after baseline rather than an unlikely effect of TTX. There was an increase in the membrane specific resistance in TTX. The reason for this is unknown, but it meant that iNaP could not be determined by simple subtraction. Attempts to account for iNaP with a Hodgkin-Huxley model of the transient sodium conductance met with mixed results. One thing to emerge was the importance of voltage shifts. Also, a large variability in previously reported values of transient sodium conductance in mossy fibre boutons made comparisons with our results difficult. Various other possible sources of error are discussed. Simulations suggest a role for iNaP in modulating the axonal attenuation of EPSPs. KEY POINTS: We used whole-cell patch clamp to estimate the stationary voltage dependence of persistent sodium-current density (iNaP) in rat hippocampal mossy fibre boutons, using a KCl-based internal (pipette) solution and correcting for the liquid junction potential (2 mV). Space-clamp errors and deterioration of the patch-clamp seal during the experiment were corrected for by compartmental modelling. Attempts to account for iNaP in terms of the transient sodium conductance met with mixed results. One possibility is that the transient sodium conductance is higher in mossy fibre boutons than in the axon shaft. The analysis illustrates the need to account for various voltage shifts (Donnan potentials, liquid junction potentials and, possibly, other voltage shifts). Simulations suggest a role for iNaP in modulating the axonal attenuation of excitatory postsynaptic potentials, hence analog signalling by dentate granule cells.

Spontaneous slow wave oscillations in extracellular field potential recordings reflect the alternating dominance of excitation and inhibition

In the resting state, cortical neurons can fire action potentials spontaneously but synchronously (Up state), followed by a quiescent period (Down state) before the cycle repeats. Extracellular recordings in the infragranular layer of cortex with a micro-electrode display a negative deflection (depth-negative) during Up states and a positive deflection (depth-positive) during Down states. The resulting slow wave oscillation (SWO) has been studied extensively during sleep and under anaesthesia. However, recent research on the balanced nature of synaptic excitation and inhibition has highlighted our limited understanding of its genesis. Specifically, are excitation and inhibition balanced during SWOs? We analyse spontaneous local field potentials (LFPs) during SWOs recorded from anaesthetised rats via a multi-channel laminar micro-electrode and show that the Down state consists of two distinct synaptic states: a Dynamic Down state associated with depth-positive LFPs and a prominent dipole in the extracellular field, and a Static Down state with negligible (≈ 0 mV $ \approx 0{\mathrm{\;mV}}$ ) LFPs and a lack of dipoles extracellularly. We demonstrate that depth-negative and -positive LFPs are generated by a shift in the balance of synaptic excitation and inhibition from excitation dominance (depth-negative) to inhibition dominance (depth-positive) in the infragranular layer neurons. Thus, although excitation and inhibition co-tune overall, differences in their timing lead to an alternation of dominance, manifesting as SWOs. We further show that Up state initiation is significantly faster if the preceding Down state is dynamic rather than static. Our findings provide a coherent picture of the dependence of SWOs on synaptic activity. KEY POINTS: Cortical neurons can exhibit repeated cycles of spontaneous activity interleaved with periods of relative silence, a phenomenon known as 'slow wave oscillation' (SWO). During SWOs, recordings of local field potentials (LFPs) in the neocortex show depth-negative deflection during the active period (Up state) and depth-positive deflection during the silent period (Down state). Here we further classified the Down state into a dynamic phase and a static phase based on a novel method of classification and revealed non-random, stereotypical sequences of the three states occurring with significantly different transitional kinetics. Our results suggest that the positive and negative deflections in the LFP reflect the shift of the instantaneous balance between excitatory and inhibitory synaptic activity of the local cortical neurons. The differences in transitional kinetics may imply distinct synaptic mechanisms for Up state initiation. The study may provide a new approach for investigating spontaneous brain rhythms.

Scaled, high fidelity electrophysiological, morphological, and transcriptomic cell characterization

The Patch-seq approach is a powerful variation of the patch-clamp technique that allows for the combined electrophysiological, morphological, and transcriptomic characterization of individual neurons. To generate Patch-seq datasets at scale, we identified and refined key factors that contribute to the efficient collection of high-quality data. We developed patch-clamp electrophysiology software with analysis functions specifically designed to automate acquisition with online quality control. We recognized the importance of extracting the nucleus for transcriptomic success and maximizing membrane integrity during nucleus extraction for morphology success. The protocol is generalizable to different species and brain regions, as demonstrated by capturing multimodal data from human and macaque brain slices. The protocol, analysis and acquisition software are compiled at https://githubcom/AllenInstitute/patchseqtools. This resource can be used by individual labs to generate data across diverse mammalian species and that is compatible with large publicly available Patch-seq datasets.

Is realistic neuronal modeling realistic?

Scientific models are abstractions that aim to explain natural phenomena. A successful model shows how a complex phenomenon arises from relatively simple principles while preserving major physical or biological rules and predicting novel experiments. A model should not be a facsimile of reality; it is an aid for understanding it. Contrary to this basic premise, with the 21st century has come a surge in computational efforts to model biological processes in great detail. Here we discuss the oxymoronic, realistic modeling of single neurons. This rapidly advancing field is driven by the discovery that some neurons don't merely sum their inputs and fire if the sum exceeds some threshold. Thus researchers have asked what are the computational abilities of single neurons and attempted to give answers using realistic models. We briefly review the state of the art of compartmental modeling highlighting recent progress and intrinsic flaws. We then attempt to address two fundamental questions. Practically, can we realistically model single neurons? Philosophically, should we realistically model single neurons? We use layer 5 neocortical pyramidal neurons as a test case to examine these issues. We subject three publically available models of layer 5 pyramidal neurons to three simple computational challenges. Based on their performance and a partial survey of published models, we conclude that current compartmental models are ad hoc, unrealistic models functioning poorly once they are stretched beyond the specific problems for which they were designed. We then attempt to plot possible paths for generating realistic single neuron models.

Optimizing ion channel models using a parallel genetic algorithm on graphical processors

We have recently shown that we can semi-automatically constrain models of voltage-gated ion channels by combining a stochastic search algorithm with ionic currents measured using multiple voltage-clamp protocols. Although numerically successful, this approach is highly demanding computationally, with optimization on a high performance Linux cluster typically lasting several days. To solve this computational bottleneck we converted our optimization algorithm for work on a graphical processing unit (GPU) using NVIDIA's CUDA. Parallelizing the process on a Fermi graphic computing engine from NVIDIA increased the speed ∼180 times over an application running on an 80 node Linux cluster, considerably reducing simulation times. This application allows users to optimize models for ion channel kinetics on a single, inexpensive, desktop "super computer," greatly reducing the time and cost of building models relevant to neuronal physiology. We also demonstrate that the point of algorithm parallelization is crucial to its performance. We substantially reduced computing time by solving the ODEs (Ordinary Differential Equations) so as to massively reduce memory transfers to and from the GPU. This approach may be applied to speed up other data intensive applications requiring iterative solutions of ODEs.

Effects of active conductance distribution over dendrites on the synaptic integration in an identified nonspiking interneuron

The synaptic integration in individual central neuron is critically affected by how active conductances are distributed over dendrites. It has been well known that the dendrites of central neurons are richly endowed with voltage- and ligand-regulated ion conductances. Nonspiking interneurons (NSIs), almost exclusively characteristic to arthropod central nervous systems, do not generate action potentials and hence lack voltage-regulated sodium channels, yet having a variety of voltage-regulated potassium conductances on their dendritic membrane including the one similar to the delayed-rectifier type potassium conductance. It remains unknown, however, how the active conductances are distributed over dendrites and how the synaptic integration is affected by those conductances in NSIs and other invertebrate neurons where the cell body is not included in the signal pathway from input synapses to output sites. In the present study, we quantitatively investigated the functional significance of active conductance distribution pattern in the spatio-temporal spread of synaptic potentials over dendrites of an identified NSI in the crayfish central nervous system by computer simulation. We systematically changed the distribution pattern of active conductances in the neuron's multicompartment model and examined how the synaptic potential waveform was affected by each distribution pattern. It was revealed that specific patterns of nonuniform distribution of potassium conductances were consistent, while other patterns were not, with the waveform of compound synaptic potentials recorded physiologically in the major input-output pathway of the cell, suggesting that the possibility of nonuniform distribution of potassium conductances over the dendrite cannot be excluded as well as the possibility of uniform distribution. Local synaptic circuits involving input and output synapses on the same branch or on the same side were found to be potentially affected under the condition of nonuniform distribution while operation of the major input-output pathway from the soma side to the one on the opposite side remained the same under both conditions of uniform and nonuniform distribution of potassium conductances over the NSI dendrite.

Kinetics of two voltage-gated K+ conductances in substantia nigra dopaminergic neurons

The substantia nigra (SN) is part of the basal ganglia which is a section in the movement circuit in the brain. Dopaminergic neurons (DA) constitute the bulk of substantia nigra neurons and are related to diseases such as Parkinson's disease. Aiming at describing the mechanism of action potential firing in these cells, the current research examined the biophysical characteristics of voltage-gated K+ conductances in the dopaminergic neurons of the SN. The outside-out configuration of the patch-clamp technique was used to measure from dopaminergic neurons in acute brain slices. Two types of K+ voltage-gated conductances, a fast-inactivating A-type-like K+ conductance (K(fast)) and a slow-inactivating delayed rectifier-like K+ conductance (K(slow)), were isolated in these neurons using kinetic separation protocols. The data suggested that a fast-inactivating conductance was due to 69% of the total voltage-gated K+ conductances, while the remainder of the voltage-gated K+ conductance was due to the activation of a slow-inactivating K+ conductance. The two voltage-gated K+ conductances were analyzed assuming a Hodgkin-Huxley model with two activation and one inactivation gate. The kinetic models obtained from this analysis were used in a numerical simulation of the action potential. This simulation suggested that K(fast) may be involved in the modulation of the height and width of action potentials initiated at different resting membrane potentials while K(slow) may participate in action potential repolarization. This mechanism may indicate that SN dopaminergic neurons may perform analog coding by modulation of action potential shape.

A numerical approach to ion channel modelling using whole-cell voltage-clamp recordings and a genetic algorithm

The activity of trans-membrane proteins such as ion channels is the essence of neuronal transmission. The currently most accurate method for determining ion channel kinetic mechanisms is single-channel recording and analysis. Yet, the limitations and complexities in interpreting single-channel recordings discourage many physiologists from using them. Here we show that a genetic search algorithm in combination with a gradient descent algorithm can be used to fit whole-cell voltage-clamp data to kinetic models with a high degree of accuracy. Previously, ion channel stimulation traces were analyzed one at a time, the results of these analyses being combined to produce a picture of channel kinetics. Here the entire set of traces from all stimulation protocols are analysed simultaneously. The algorithm was initially tested on simulated current traces produced by several Hodgkin-Huxley–like and Markov chain models of voltage-gated potassium and sodium channels. Currents were also produced by simulating levels of noise expected from actual patch recordings. Finally, the algorithm was used for finding the kinetic parameters of several voltage-gated sodium and potassium channels models by matching its results to data recorded from layer 5 pyramidal neurons of the rat cortex in the nucleated outside-out patch configuration. The minimization scheme gives electrophysiologists a tool for reproducing and simulating voltage-gated ion channel kinetics at the cellular level.

Voltage-gated ion channels affect neuronal integration of information. Some neurons express more than ten different types of voltage-gated ion channels, making information processing a highly convoluted process. Kinetic modelling of ion channels is an important method for unravelling the role of each channel type in neuronal function. However, the most commonly used analysis techniques suffer from shortcomings that limit the ability of researchers to rapidly produce physiologically relevant models of voltage-gated ion channels and of neuronal physiology. We show that conjugating a stochastic search algorithm with ionic currents measured using multiple voltage-clamp protocols enables the semi-automatic production of models of voltage-gated ion channels. Once fully automated, this approach may be used for high throughput analysis of voltage-gated currents. This in turn will greatly shorten the time required for building models of neuronal physiology to facilitate our understanding of neuronal behaviour.